Question

1. oh henry candy bars have a mean mass of 250 g with a standard deviation of 5 grams. assuming a normal distribution, answer the following questions.

a) what percentage of oh henry bars will have a mass between 245 g and 255 g? (1 mark)

Explanation:

Step1: Calculate the z - scores

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 250\) (mean) and \(\sigma=5\) (standard deviation).
For \(x = 245\), \(z_1=\frac{245 - 250}{5}=\frac{-5}{5}=-1\).
For \(x = 255\), \(z_2=\frac{255 - 250}{5}=\frac{5}{5}=1\).

Step2: Use the standard normal distribution table

We know that the probability \(P(-1<Z<1)\) can be found using the property \(P(-1 < Z < 1)=P(Z < 1)-P(Z<-1)\).
From the standard normal distribution table, \(P(Z < 1)=0.8413\) and \(P(Z<-1)=0.1587\).
So \(P(-1 < Z < 1)=0.8413-0.1587 = 0.6826\).

Answer:

\(68.26\%\)